Overview

Effect sizes complement p-values: they answer “how big is the effect?” rather than “is there an effect at all?”. MORIE exposes the standard families used in carceral, public-health, and sociolegal research.

Cohen’s d (continuous, two-group)

library(rmorie)
set.seed(7)
group_a <- rnorm(60, mean = 0.0)
group_b <- rnorm(60, mean = 0.6)

d <- morie_cohens_d(group_a, group_b)
d
#> [1] -0.5043227

Cohen’s d expresses the difference between two means in pooled standard-deviation units. Conventional benchmarks: 0.2 small, 0.5 medium, 0.8 large.

Cramer’s V (categorical association)

tab <- matrix(c(20, 10, 30,
                15, 25, 35), nrow = 2, byrow = TRUE)
v <- morie_cramers_v(tab)
v
#> [1] 0.209657

Cramer’s V scales the chi-square statistic to a 0–1 association measure for contingency tables. It is particularly useful for the provincial-vs-federal Mandela-rate cross-comparisons in MRM.

Omega-squared (one-way ANOVA)

Omega-squared is a less-biased effect-size estimator than eta-squared for a one-way ANOVA design.

morie_omega_squared(f_stat = 5.2, df_between = 2, df_within = 87, n = 90)
#> [1] 0.08536585

Proportion confidence intervals

For a binomial proportion, MORIE exposes Wilson, Clopper–Pearson exact, and Wald CIs. Wilson is the default and is what we recommend in published papers (it has better small-sample coverage than Wald).

morie_proportion_ci(35, 100)                       # Wilson, 95% CI
#> $p_hat
#> [1] 0.35
#> 
#> $ci_lower
#> [1] 0.2636425
#> 
#> $ci_upper
#> [1] 0.4474556
morie_proportion_ci(35, 100, method = "exact")     # Clopper-Pearson
#> $p_hat
#> [1] 0.35
#> 
#> $ci_lower
#> [1] 0.2572938
#> 
#> $ci_upper
#> [1] 0.4518494
morie_proportion_ci(35, 100, method = "wald")      # Wald
#> $p_hat
#> [1] 0.35
#> 
#> $ci_lower
#> [1] 0.2565157
#> 
#> $ci_upper
#> [1] 0.4434843

E-value (sensitivity analysis)

morie_e_value(rr = 2.0)
#> $morie_e_value
#> [1] 3.414214
#> 
#> $e_value_ci
#> [1] NA

The E-value is the minimum strength of association that an unmeasured confounder would need on both treatment and outcome to fully explain away an observed risk ratio.

Where to go next

For survey-weighted versions of morie_cohens_d and morie_cramers_v, see the survey-weighted vignette.
For full causal-inference workflows that include ATE / ATT / ATC effect sizes with CIs, see the causal-inference vignette.